If $^{n} C_{12} =^{n} C_{8}$ then is equal to

12

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26

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6

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20

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Solution

The correct option is B $20$
$^{n} C_{12} =^{n} C_{8}$
$\frac{n!}{12! (n - 12)!} = \frac{n!}{8! (n - 8)!}$
$\frac{1}{12 \times 11 \times 10 \times 9 \times 8! (n - 12)!} = \frac{1}{8! (n - 8) \times (n - 9) (n - 10) (n - 11) (n - 12)!}$
$⟹ (n - 8) (n - 9) (n - 10) (n - 11) = 12 \times 11 \times 10 \times 9$
$∴ n - 8 = 12$
$n = 8 + 12$
$n = 20$

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